To solve this problem, we need to distribute 9 different games among Wainah (W), Jingyi (J), and Hebe (H) such that each receives an odd number of games. The possible distributions of games are (1, 1, 7), (1, 7, 1), (7, 1, 1), (1, 3, 5), (1, 5, 3), (3, 1, 5), (3, 5, 1), (5, 1, 3), (5, 3, 1), and (3, 3, 3).

We calculate the number of ways for each distribution:

1. For (1, 1, 7):
   egin{align*} 9C_1 imes 8C_1 imes 1C_1 &= 72 ext{(This is multiplied by 3 for permutations of (1, 1, 7))} ext{Total} &= 72 imes 3 = 216 ext{ways} ext{(for each permutation)} ext{Total for all permutations} &= 216
2. For (1, 3, 5):
   egin{align*} 9C_1 imes 8C_3 imes 5C_1 &= 504 ext{(This is multiplied by 6 for permutations of (1, 3, 5))} ext{Total} &= 504 imes 6 = 3024 ext{ways} ext{(for each permutation)} ext{Total for all permutations} &= 3024
3. For (3, 3, 3):
   egin{align*} 9C_3 imes 6C_3 imes 3C_3 &= 1680 ext{(This is multiplied by 1 as all are equal)} ext{Total} &= 1680 ext{ways} ext{(for each permutation)} ext{Total for all permutations} &= 1680

Adding all these possibilities gives the total number of ways:

egin{align*} 216 + 3024 + 1680 &= 4920 ext{ways} ext{(total)} ext{Thus, the total number of ways is } 4920. ext{This matches the mark scheme.}